When playing the AZ supporter, do I put all Pokemon stages into my hand, or just the Basic or highest stage?
You put all of the Pokemon cards into your hand, including all Stages and Mega cards.
Source: Phantom Forces FAQ (2014-11-13), TPCi Rules Team (2014-11-13)

Relevant cards

Note: All applicable cards may not be listed below.
XY4_117
XY4_91